smetuwh

2022-09-06

Consider the following.
22, 11, 33, 24, 21
Compute the population standard deviation of the numbers.

Haylee Branch

From the given information, the data is 22, 11, 33, 24, 21.
Use the following formula to compute the population mean:
$\mu =\frac{\sum X}{N}$
Here, N total number of observations.
Use the following formula to compute the population standard deviation:
$\sigma =\sqrt{\frac{\sum \left(x-\mu {\right)}^{2}}{N}}$
Substitute the values in the formula.
$\mu =\frac{\sum x}{N}\phantom{\rule{0ex}{0ex}}=\frac{22+11+33+24+21}{5}\phantom{\rule{0ex}{0ex}}=\frac{111}{5}\phantom{\rule{0ex}{0ex}}=22.2$
Use the following formula to compute the population standard deviation:
$\sigma =\sqrt{\frac{\left(22-22.2{\right)}^{2}+\left(11-22.2{\right)}^{2}+\left(33-22.2{\right)}^{2}+\left(24-22.2{\right)}^{2}+\left(21-22.2{\right)}^{2}}{5}}\phantom{\rule{0ex}{0ex}}=\sqrt{\frac{0.04+125.44+116.64+3.24+1.44}{5}}\phantom{\rule{0ex}{0ex}}=\sqrt{49.36}\phantom{\rule{0ex}{0ex}}=7.025667\phantom{\rule{0ex}{0ex}}\approx 7.0257$
Therefore, the population standard deviation is 7.0257.

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